Using ratio test and getting R and interval

**gabet16941** · March 31st, 2009, 03:36 PM

Use the ratio test to find the radius of convergence and interval of convergence of the power series.

what are the R and the interval

**HallsofIvy** · March 31st, 2009, 04:23 PM

The ratio test says that if [tex]lim_{n\rightarrow \infty}\frac{a_{n+1}}{a_n}< 1[tex] then the series $\sum a_n$ converges.
Here $a_n= \frac{4^n(x-1)^n}{n}$ so $a_{n+1}= \frac{4^{n+1}(x-1)^{n+1}}{n+1}$ and $\frac{a_{n+1}}{a_n}= \frac{4^{n+1}(x-1)&{n+1}}{n+1}\frac{n}{4^n(x-1)^n}$ $= 4(x-1)\frac{n+1}{n}$ . What is the limit of that as n goes to infinity? For what values of x is that limit less than 1?

**gabet16941** · March 31st, 2009, 05:57 PM

i got the radius to be 1/4 and upper part of interval to be 5/4 but cant seem to get lower part if the interval

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